Providing an Analytical Model in Determining Nanofluids

The inﬂuence of temperature, mean nanoparticle size and the nanoparticle concentration on the dynamic viscosities of nanofluids are investigated in an analytical method followed by introduction of modified equations for calculating the nanoﬂuids’ viscosities. A new correlation is developed for effective viscosity based on the previous model where the Brownian movement of the nanoparticles is considered as the key mechanism. In previous studies, the proposed models were not appropriate for nanoparticles larger than 36 nm. They were also focused on low concentrations of nanoparticles up to 5%. The possibility of homogeneous dispersion of the nanoparticles and the Stokes law are observed here. This new model is explained in terms of temperature, mean nanoparticle diameter, nanoparticle volume concentration and both the nanoparticle and base fluid thermophysical characteristics for the effective viscosity of nanofluids. A combined correction factor is introduced to take into account the simpliﬁcation for a free stream boundary condition outside the boundary layer. A good agreement is observed between the effective viscosity obtained in this new model and those of recorded experiments conducted for different nanoﬂuids. The results show that the present model is valid for large volume concentration (0% < φ